Simulation intelligence: Towards a new generation of scientific methods

A Lavin, D Krakauer, H Zenil, J Gottschlich… - arXiv preprint arXiv …, 2021 - arxiv.org
The original" Seven Motifs" set forth a roadmap of essential methods for the field of scientific
computing, where a motif is an algorithmic method that captures a pattern of computation …

[图书][B] Uncertainty quantification: theory, implementation, and applications

RC Smith - 2024 - SIAM
Uncertainty quantification serves a central role for simulation-based analysis of physical,
engineering, and biological applications using mechanistic models. From a broad …

Bayesian probabilistic numerical methods

J Cockayne, CJ Oates, TJ Sullivan, M Girolami - SIAM review, 2019 - SIAM
Over forty years ago average-case error was proposed in the applied mathematics literature
as an alternative criterion with which to assess numerical methods. In contrast to worst-case …

Physics-informed Gaussian process regression generalizes linear PDE solvers

M Pförtner, I Steinwart, P Hennig, J Wenger - arXiv preprint arXiv …, 2022 - arxiv.org
Linear partial differential equations (PDEs) are an important, widely applied class of
mechanistic models, describing physical processes such as heat transfer, electromagnetism …

Position paper: Bayesian deep learning in the age of large-scale ai

T Papamarkou, M Skoularidou, K Palla… - arXiv e …, 2024 - ui.adsabs.harvard.edu
In the current landscape of deep learning research, there is a predominant emphasis on
achieving high predictive accuracy in supervised tasks involving large image and language …

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI

T Papamarkou, M Skoularidou, K Palla… - … on Machine Learning, 2024 - openreview.net
In the current landscape of deep learning research, there is a predominant emphasis on
achieving high predictive accuracy in supervised tasks involving large image and language …

Posterior and computational uncertainty in gaussian processes

J Wenger, G Pleiss, M Pförtner… - Advances in …, 2022 - proceedings.neurips.cc
Gaussian processes scale prohibitively with the size of the dataset. In response, many
approximation methods have been developed, which inevitably introduce approximation …

[图书][B] Probabilistic Numerics: Computation as Machine Learning

P Hennig, MA Osborne, HP Kersting - 2022 - books.google.com
Probabilistic numerical computation formalises the connection between machine learning
and applied mathematics. Numerical algorithms approximate intractable quantities from …

Bayesian ODE solvers: the maximum a posteriori estimate

F Tronarp, S Särkkä, P Hennig - Statistics and Computing, 2021 - Springer
There is a growing interest in probabilistic numerical solutions to ordinary differential
equations. In this paper, the maximum a posteriori estimate is studied under the class of ν ν …

Parallel-in-time probabilistic numerical ODE solvers

N Bosch, A Corenflos, F Yaghoobi, F Tronarp… - Journal of Machine …, 2024 - jmlr.org
Probabilistic numerical solvers for ordinary differential equations (ODEs) treat the numerical
simulation of dynamical systems as problems of Bayesian state estimation. Aside from …